论文标题
模块化形式的三倍的对称$ p $ adadic符号
A symmetric $p$-adic symbol for triples of modular forms
论文作者
论文摘要
2014年，达尔蒙（Darmon）和罗特（Rotger）定义了Garrett-Rankin Triple Product $ P $ -ADIC $ L $ - 功能，并将其与某些对角线周期的图像相关联，在$ p $ adic-adic Abel-Jacobi地图下。我们基于此$ p $ -adic $ l $ - 功能引入了一个新的$ p $ - adiC三重符号，并在将三个输入模块化表单放置时表明它满足对称关系。我们还提供了说明这种对称属性的计算示例。为此，我们扩展了Lauder的算法，以允许对几乎过度会议模块化形式的普通投影（不仅是过度授权的模块化形式）以及在非零斜率空间上的某些投影。我们的工作还提供了一种有效的方法来计算更高重量的某些庞加莱配对，这可能具有独立感兴趣。
In 2014, Darmon and Rotger defined the Garrett-Rankin triple product $p$-adic $L$- function and related it to the image of certain diagonal cycles under the $p$-adic Abel- Jacobi map. We introduce a new $p$-adic triple symbol based on this $p$-adic $L$- function and show that it satisfies symmetry relations, when permuting the three input modular forms. We also provide computational examples illustrating this symmetry property. To do so, we extend Lauder's algorithm to allow for ordinary projections of nearly overconvergent modular forms -- not just overconvergent modular forms -- as well as certain projections over spaces of non-zero slope. Our work also gives an efficient method to calculate certain Poincaré pairings in higher weight, which may be of independent interest.
